It’s great that you’ve proven things work, but using a better battery.
9v batteries have notoriously bad capacity.
What type of battery were you using? Was it “fresh” just out of the packet? What was it’s shelf-life date printed on the packet? How far out was that date?
How much current does your entire system draw? What else do you have connected and how much do each of those draw?
You also need to change your program to figure out what part of your system is stopping responding, is it the MP3 player not doing it’s thing or is it the SD card (I think you’re using that?). You need to build some debugging into this - complaining isn’t helping
I have no idea exactly the “typical” capacity of the 9v battery you are using. A quick Bing on the internet shows some “standard” rechargeable nimh batts being in the 200mAh range. If you’ve only used a standard alkaline you may be getting 150mAh or less.
Here’s some maths for you though. Fez Domino, on it’s own, when running requires 110mA. That means with a 200mAh rechargeable battery, at full capacity, and 100% efficiency all along the way, will run just the domino for 109 minutes. You plug in the MP3 component - more current consumed. Read the SD card - more current. What’s worse is that you’re actually burning up some of the power in heat because you’re actually feeding the 9v into a regulator that is controlling the voltage down to 5v and then 3v3, which is another loss. So you’re not doing yourself a favour in trying to use a 9v battery as a power source. Find a bigger capacity 9v battery (yes, that will most likely mean bigger size too) and you’ll be better off. Find a better way to generate the required voltage and you’re better off. Did you know a rechargeable nimh AA battery is typically 2000mAh or more? Gee, that’s a lot more capacity if you need it and it’s small too!
I don’t want to dishearten you or anything, but mobile phone manufacturers the world over spend gazillions of dollars making sure their devices are drawing the absolute minimum current possible, so they can add minutes of talk-time to their selling points, while constraining their battery capacities so the handset doesn’t get bulky or heavy. They do all this by using specialist chips and understanding the circuit inside-out and screwing down every single current consumer possible to the minimum. You at home can’t compete with that, there are compromises you will have to make. Same goes for MP3 players, the makers buy specialist parts that run at ultra low voltages so they don’t have to convert or regulate power any more than necessary. Can you make a Domino a usable, portable MP3 player? Hell yes. Can you make it last as long as your iriver clix or zune or ipod nano, sure, but at the expense of portability. Can you make a Domino match the performance of an iriver, not likely unless you were an engineer who worked on the iriver in the first place!